Mathematical modelling of tumour volume dynamics in response to stereotactic ablative radiotherapy for non-small cell lung cancer

Abstract

This paper reports a modelling study of tumour volume dynamics in response to stereotactic ablative radiotherapy (SABR). The main objective was to develop a model that is adequate to describe tumour volume change measured during SABR, and at the same time is not excessively complex as lacking support from clinical data. To this end, various modelling options were explored, and a rigorous statistical method, the Akaike information criterion, was used to help determine a trade-off between model accuracy and complexity. The models were calibrated to the data from 11 non-small cell lung cancer patients treated with SABR. The results showed that it is feasible to model the tumour volume dynamics during SABR, opening up the potential for using such models in a clinical environment in the future.

Modelling and Bayesian adaptive prediction of individual patients’ tumour volume change during radiotherapy

“…As expected, different patients may respond to radiotherapy very differently, a phenomenon also observed in our previous report of modelling SABR patients (Tariq et al 2015), and other related studies (Seibert et al, 2007;Chvetsov et al, 2009;Chvetsov et al, 2014). The inter-patient variability…”

“…The first important observation is that the 2-Exp model appears to be a good option for describing noted that similar models have been used in other tumour volume modelling studies (Chvetsov et al, 2014;Tariq et al, 2015).…”

“…This section briefly presents the mathematical models used to describe the change of GTV over time, and the AIC method for model selection, similar to our previous modelling study for SABR (Tariq et al, 2015) and other related work (Chvetsov et al, 2014). The focus will then be on presenting a Bayesian model adaptation algorithm for prediction.…”

“…We follow the previous study of modelling tumour volume during SABR for model calibration and selection (Tariq et al, 2015). Specifically, the models listed in Table 1  The carrying capacity, ( ), varies from patient to patient, and so do the bounds.…”

“…An empirical regression model was presented by Seibert et al (2007) for lung cancer (both non-small cell and small cell) treated by helical Tomotherapy. Recently, we reported a radiobiological modelling study for stereotactic ablative radiotherapy (SABR) of NSCLC (Tariq et al, 2015), which emphasised the need for a systems approach to the selection of proper models. However, these studies have been limited to fitting the models to clinical data.…”